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Decimal expansion of 0.5250984..., a real fixed point of the iteration s = zetahurwitz(s, A324859).
2

%I #7 Mar 18 2019 13:05:55

%S 5,2,5,0,9,8,4,2,4,6,2,8,8,9,2,5,7,2,1,1,5,4,3,8,9,1,2,3,9,5,8,5,1,3,

%T 1,6,4,2,9,6,3,1,1,0,7,5,4,8,7,9,6,3,2,0,1,8,8,7,0,2,4,4,4,9,1,7,8,5,

%U 4,5,6,9,1,4,0,6,5,5,2,5,1,2,7,7,0,0,7,6,0,9,1,1,9,5,2,7,2,0,9,5

%N Decimal expansion of 0.5250984..., a real fixed point of the iteration s = zetahurwitz(s, A324859).

%C For real values of the parameter "a" between 0 and 1, a real fixed point "s" of the iterated Hurwitz zeta function [s = zetahurwitz(s, a)] lies on a curve that passes through A069857 (-0.295905...) and has a maximum tending toward 1. This curve has inflection points for a = 0.1990753... (A324859) or 0.91964... . The fixed point "s" on this curve for the iteration "s = zetahurwitz(s, A324859)" is 0.5250984... .

%e 0.525098424628892572115438912395851316429631107548...

%o (PARI) { A324859 = solve(t = 1/16, 1/2, derivnum(x = t, solve(v = -1, 1 - x, v - zetahurwitz(v, x)), 2); ); solve(v = -1, 1 - A324859, v - zetahurwitz(v, A324859)) }

%Y Cf. A324859, A069857, A069995.

%K nonn,cons

%O 0,1

%A _Reikku Kulon_, Mar 18 2019